In an electrophotographic apparatus, if an FM modulation type dither matrix is used, it is difficult to form an independent 1 pixel (for example, 1 pixel of 600 dpi) in a stable state with the same resolution as the printer (1 dot of 600 dpi is reproduced by the printer of 2400 dpi). Thus, a high-quality image cannot be obtained. For this reason, in an image output apparatus, such as an electrophotographic apparatus, an AM modulation type dither matrix is used, and gradation is reproduced on the basis of the area in units of a plurality of pixels combined. Thereby, a stable image is obtained. AM modulation type dither methods include various shape-type methods, such as a halftone dot type, a line type, and a chain type. These methods, however, are essentially the same in that a plurality of dots are gathered in a given direction, thereby reproducing the gradation.
In order to increase the number of pseudo gradation levels to such a level as to reproduce a visually satisfactory image, it should suffice if the basic size of a halftone dot of a threshold matrix is increased. However, as the basic size of the halftone dot becomes greater, the resolution decreases. Electrophotography does not have a high resolution of several thousand dpi which is the resolution of the printer. Currently dominant type electrophotography has a low resolution of about 600 dpi. There are too many geometrical restrictions in order to obtain satisfactory gradation reproduction by creating halftone dots with a low resolution and a given angle and line number (about 100 to 200). If a screen is forcedly created while ignoring a geometrical position error in a digital arithmetic operation, various problems may be caused. For example, if halftoning is executed using the created threshold matrix, geometrical errors of many halftone centers at the positions on the two-dimensional plane are caused. Consequently, with respect to an image which is formed on the final print surface, textures, which are unsightly, occur due to geometrical errors at given gradation levels to increase granularity.
As methods for improving precision in forming the halftone dots and visually satisfying the gradation, a virtual halftone technique disclosed in U.S. Pat. No. 5,155,599 and Japanese Patent Application Publication (JP-A) No. 2003-234900 is known.
In the image processing apparatus of the electrophotographic system whose resolution is about 600 dpi, a phase shift caused by digital restriction on a two-dimensional space by the virtual halftone dot itself cannot be ignored. For this reason, a subtle cyclic shift of the halftone dot center is visually detected, and roughness or granularity of the image is recognized.
In recent electrophotography, even if a screen of about 200 lines is used, the gradation can be reproduced while the granularity can be prevented from being deteriorated. However, when the resolution is about 600 dpi, a screen of about 200 lines is created with a low degree of freedom, regardless of whether or not it is a binary or multi-value output. In the case of color superimposition of four colors, there is almost no alternative to screen specification (line number and angle). In the color superimposition of four colors, a considerably discrete set of line number and angle is obtained, and color moire is likely to occur according to the color.